Sampling apparatus, sampling method and recording medium

ABSTRACT

Provided is a sampling apparatus that samples a signal under measurement, including a sampling section that samples the signal under measurement with a plurality of sampling phases at non-uniform intervals for each sampling repetition cycle; and an inverting section that cancels out a replica that is not an observation target, from among the replicas in a sampling band of the signal under measurement and the replicas in the sampling band of a frequency component of the signal under measurement, by inverting signs of values of the signal under measurement sampled with at least one sampling phase from among the plurality of sampling phases.

BACKGROUND

1. Technical Field

The present invention relates to a sampling apparatus, a samplingmethod, and a recording medium storing thereon a program. In particular,the present invention relates to a sampling apparatus, a samplingmethod, and a recording medium storing thereon a program for sampling asignal under measurement.

2. Related Art

A conventional sampling method, known as 2^(nd) order sampling, uses twosampling timings having identical sampling frequencies and differentphases, as shown in, for example, Arthur Kohlenberg, “ExactInterpolation of Band-limited Functions,” Journal of Applied Physics,Vol. 24, No. 12, December 1953. Sampling at N target points in eachsampling cycle is also proposed, as in, for example, Kuroda Tohru, KidaTakuro, “Relations between the possibility of restoration ofbandpass-type band-limited waves by interpolation and arrangement ofsampling points”, Denki Tsushin Gakkai Ronbunsho, Vol J67-A, pp.717-724, 1984.

With these conventional methods, N non-uniform sampling timings are setto one cycle. The continuous time function of the signal undermeasurement is then obtained by performing a convolution operationbetween sample data obtained by repeatedly sampling the signal undermeasurement over a plurality of cycles and the sampling function derivedfrom the phase of each sampling timing. The discrete-time waveform datais obtained by sequentially substituting the discrete-time having thetarget time intervals into the continuous time function.

Since conventional methods require derivation of the sampling functionand sequential calculation of the values of the waveform data bysubstituting time into the sampling function, the signal processingbecomes complicated.

An interleave method is known for acquiring a signal having a high bandby alternately and uniformly deviating sampling timings of a pluralityof AD converters. With this method, however, the data amount acquiredper unit time increases relative to the number of AD converters, andtherefore the circuit size of the memory circuit at the final stage mustbe increased.

Another method is known for acquiring a signal having a high band byobtaining a signal that is down-converted by a mixer. With this method,however, a circuit such as a local oscillator and a filter must beprovided, thereby increasing the circuit size.

Undersampling is yet another method for acquiring a signal having a highband. Undersampling, however, imposes a limit on the acquirable band.For example, if there is one AD converter, the acquirable signal islimited to having a bandwidth less than fs/2 and cannot cross multiplesof (fs/2), where fs is the sampling frequency. Even if two AD convertersperform undersampling through interleaving, a signal crossing a multipleof (fs/2) cannot be acquired.

Cited Documents:

Arthur Kohlenberg, “Exact Interpolation of Band-limited Functions,”Journal of Applied Physics, Vol. 24, No. 12, December 1953.

Kuroda Tohru, Kida Takuro, “Relations between the possibility ofrestoration of bandpass-type band-limited waves by interpolation andarrangement of sampling points”, Denki Tsushin Gakkai Ronbunsho, VolJ67-A, pp. 717-724, 1984.

SUMMARY

Therefore, it is an object of an aspect of the innovations herein toprovide a sampling apparatus, a sampling method, and a recording mediumstoring thereon a program, which are capable of overcoming the abovedrawbacks accompanying the related art. The above and other objects canbe achieved by combinations described in the independent claims. Thedependent claims define further advantageous and exemplary combinationsof the innovations herein.

According to a first aspect related to the innovations herein, oneexemplary sampling apparatus may include a sampling apparatus thatsamples a signal under measurement, including a sampling section thatsamples the signal under measurement at a plurality of sampling phasesat non-uniform intervals for each sampling repetition cycle; and aninverting section that cancels out a replica that is not an observationtarget, from among the replicas in a sampling band of the signal undermeasurement and the replicas in the sampling band of a negativefrequency component of the signal under measurement, by inverting a signof a value of the signal under measurement sampled at at least one ofthe plurality of sampling phases.

According to a second aspect related to the innovations herein, oneexemplary sampling method may include a method for sampling a signalunder measurement, including the steps of sampling the signal undermeasurement at a plurality of sampling phases at non-uniform intervalsfor each sampling repetition cycle; and canceling out a replica that isnot an observation target, from among the replicas in a sampling band ofthe signal under measurement and the replicas in the sampling band of anegative frequency component of the signal under measurement, byinverting a sign of a value of the signal under measurement sampled atat least one of the plurality of sampling phases.

According to a third aspect related to the innovations herein, oneexemplary recording medium may include a recording medium storingthereon a program that, when performed by a computer, causes thecomputer to control a sampling apparatus to sample a signal undermeasurement. The sampling apparatus includes a sampling section and aninverting section. The program causes the sampling apparatus to (i)cause the inverting section to sample the signal under measurement at aplurality of sampling phases at non-uniform intervals for each samplingrepetition cycle; and (ii) cause the inverting section to cancel out areplica that is not an observation target, from among the replicas in asampling band of the signal under measurement and the replicas in thesampling band of a negative frequency component of the signal undermeasurement, by inverting a sign of a value of the signal undermeasurement sampled at at least one of the plurality of sampling phase.

The summary clause does not necessarily describe all necessary featuresof the embodiments of the present invention. The present invention mayalso be a sub-combination of the features described above. The above andother features and advantages of the present invention will become moreapparent from the following description of the embodiments taken inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a configuration of a sampling apparatus 10 according to thepresent embodiment.

FIG. 2 shows the performance of the sampling apparatus 10 according tothe present embodiment.

FIG. 3 shows a pass band of the band limiting section 110 according tothe present embodiment.

FIG. 4 shows a performance timing of the sample processing section 115according to the present embodiment.

FIG. 5 shows replicas occurring in the signal under measurement sampledby the AD converter 125 according to the present embodiment.

FIG. 6 shows frequency bands in which the replicas are canceled out bythe sample processing section 115 according to the present embodiment.

FIG. 7A shows a signal under measurement input into the sampleprocessing section 115 of the present embodiment; FIG. 7B shows a signaloutput from the sample processing section 115; and FIG. 7C shows areproduction of the frequency component 730 of the signal undermeasurement based on the synthesized replica 720 e.

FIG. 8A shows another example of the signal under measurement input intothe sample processing section 115 of the present embodiment; and FIG. 8Bshows another example of a signal output by the sample processingsection 115 of the present embodiment.

FIG. 9 shows a configuration of the sample processing section 115according to a first modification of the present embodiment.

FIG. 10 shows a configuration of the sample processing section 115according to a second modification of the present embodiment.

FIG. 11 shows a configuration of the sample processing section 115according to a third modification of the present embodiment.

FIG. 12 shows a configuration of the sample processing section 115according to a fourth modification of the present embodiment.

FIG. 13 shows an example of a hardware configuration of a computer 1900according to the present embodiment.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Hereinafter, some embodiments of the present invention will bedescribed. The embodiments do not limit the invention according to theclaims, and all the combinations of the features described in theembodiments are not necessarily essential to means provided by aspectsof the invention.

FIG. 1 shows a configuration of a sampling apparatus 10 according to thepresent embodiment. The sampling apparatus 10 samples a signal undermeasurement to generate waveform data of the signal under measurement.More specifically, the sampling apparatus 10 samples the signal undermeasurement by repeatedly performing the sampling process at a pluralityof sampling phases at non-uniform intervals, for each samplingrepetition cycle. Here, the sampling apparatus 10 selects each samplingphase to be suitable for the frequency domain of the signal undermeasurement, and/or changes the sign of the sampled data as appropriate.In this way, the sampling apparatus 10 can cancel out replicas that arenot observation targets from among the replicas of the signal undermeasurement and the replicas of the negative frequency component of thesignal under measurement caused by the sampling. Therefore, the samplingapparatus 10 can cause the replicas being observed to remain in thesampled data sequence, and can then generate waveform data of the signalunder measurement based on these replicas.

The sampling apparatus 10 is provided with an input section 100, asetting section 105, a band limiting section 110, a sample processingsection 115, a storage section 140, and a waveform generating section150. The input section 100 receives the observation band of the signalunder measurement as input. Based on the input observation band, thesetting section 105 sets a passable frequency band for the band limitingsection 110, sets a plurality of sampling phases for a clock controlsection 120 in the sample processing section 115, sets a multiplexmethod of the sampled data for a multiplexer 130 in the sampleprocessing section 115, and sets information for an inverting section135 in the sample processing section 115 that indicates the samplingphases at which the inverting section inverts the values of the signalunder measurement, from among the plurality of sampling phases.

The band limiting section 110 receives the signal under measurement,which is an analog signal, and allows a frequency component of apassable frequency domain designated by the setting section 105 to passthrough to the sample processing section 115. Frequency components thatare outside of this passable frequency domain are damped or blocked. Ifthe frequency domain of the signal under measurement is determined inadvance, the band limiting section 110 may be omitted from theconfiguration of the sampling apparatus 10.

The sample processing section 115 receives the signal under measurementhaving a frequency domain that is limited by the band limiting section110 to be within the observation band. The sample processing section 115outputs sample data obtained by sampling the received signal undermeasurement at non-uniform intervals. In this way, the sample processingsection 115 cancels out unnecessary replicas in the signal undermeasurement caused by the sampling, and outputs sample data in which thetarget replicas remain. The sample processing section 115 includes theclock control section 120, AD converters 125-1, 125-2, the multiplexer130, and the inverting section 135.

The clock control section 120 receives a setting from the settingsection 105 to generate a plurality of sampling clocks that repeatedlysample the signal under measurement in each cycle at a plurality ofsampling phases at non-uniform intervals. The plurality of AD converters125 are examples of sampling sections, and sample the signal undermeasurement with each of the plurality of sampling clocks. Each ADconverter 125 is an example of a sampler. The AD converters are disposedto correspond respectively to a plurality of sampling clocks, and outputdigital sample data obtained by sampling the analog signal undermeasurement at corresponding sampling clocks, for each sampling clock.In the present embodiment, the sample processing section 115 includestwo AD converters 125, but the sample processing section 115 may includethree or more AD converters 125.

The multiplexer 130 switches between selecting the sample data from theplurality of AD converters 125 and the constant 0, and multiplexes theresulting data to output multiplexed sample data. The inverting section135 receives a setting from the setting section 105 to invert the signof the sample data values, which are values of the signal undermeasurement sampled at at least one sampling phase from among theplurality of sampling phases, as necessary. Depending on the setting,the inverting section 135 need not invert the sign of any of the datavalues. The inverting section 135 may be omitted from the configurationof the sampling apparatus 10, in which case the sampling apparatus 10may cancel out the unnecessary replicas by selecting sampling phaseswithout inverting the signs of the data values.

The storage section 140 stores the sample data output by the sampleprocessing section 115. For example, the storage section 140 includes amemory onto which the storage section 140 sequentially stores, atconsecutive addresses, a data sequence of the sample data outputsequentially by the sample processing section 115. Instead of thisexample or in addition to this example, the storage section 140 may bedivided to correspond to each AD converter 125, and the storage section140 may temporarily store the sample data output by each AD converter125. The storage section 140 may be omitted from the configuration ofthe sampling apparatus 10.

The waveform generating section 150 generates waveform data of thesignal under measurement based on the sample data read from the storagesection 140. More specifically, the waveform generating section 150generates the waveform data of the signal under measurement based on thetarget replicas received from the sample processing section 115. Thewaveform generating section 150 includes a Fourier transform section155, an extracting section 160, a frequency converting section 162, andan inverse Fourier transform section 165.

The Fourier transform section 155 reads the sample data, which is theoutput signal of the inverting section 135, from the storage section 140and Fourier transforms this data into the frequency domain. Theextracting section 160 extracts the target replicas from the frequencydomain. The frequency converting section 162 generates the signal undermeasurement in the frequency domain, based on the target replicas in thefrequency domain. The inverse Fourier transform section 165 inverseFourier transforms the signal under measurement in the generatedfrequency domain to generate waveform data of the signal undermeasurement in the time domain.

FIG. 2 shows the performance of the sampling apparatus 10 according tothe present embodiment.

First, the input section 100 receives the observation band of the signalunder measurement as input (S200). Here, a user may input theobservation band of the signal under measurement into the input section100. If the sampling apparatus 10 is capable of sampling with a broadspectrum, such as by sweeping, which involves sampling the signal undermeasurement while alternating the observation band, the samplingapparatus 10 may receive designation for a plurality of observationbands for each measurement from the control section in the samplingapparatus 10.

Next, the setting section 105 receives the observation band from theinput section 100 and provides a setting for the band limiting section110, the clock control section 120, the multiplexer 130, and theinverting section 135 according to the observation band (S205). Thesetting section 105 sets the observation band to be the pass band of theband limiting section 110.

The setting section 105 sets, for the clock control section 120, aplurality of sampling phases at determined non-uniform intervals suchthat replicas that are not observation targets cancel each other out,from among the replicas of the negative frequency component and thereplicas of the signal under measurement in the observation band havinga bandwidth that is less than that of the sampling band. Here, thesampling band serves to generate the waveform data of the signal undermeasurement. Therefore, the sampling band is a frequency band from whichare extracted the replicas of the portion of the signal undermeasurement that does not interfere with other replicas, namely thepositive frequency component or the negative frequency component of thesignal under measurement. This sampling band may have a frequency-placethat is lower than, or no greater than, that of the observation band.The sampling band may have a frequency-place that is fixed regardless ofthe observation band, or may have a frequency-place that can changeaccording to the observation band. In the present embodiment, where foursampling phases are used, for example, the sampling band is a frequencyband from 0 to less than double the sampling repetition frequency orfrom the sampling repetition frequency to triple the sampling repetitionfrequency.

The setting section 105 sets the order in which the multiplexer 130selects the constant 0 and the sample data output from each AD converter125. The setting section 105 sets, for each sampling phase, whether theinverting section inverts the signs of the values of the signal undermeasurement sampled at each sampling phase, based on the observationband. The setting section 105 may instead set the inverting section toinvert the sign of the values of the signal under measurement at all ofthe sampling phases, based on the observation band. In this way, theinverting section 135 can cancel out the replicas in the sampling bandthat are not observation targets. The setting section 105 may cancel outall of the replicas in the sampling band that are not observationtargets by a combination of selecting the sampling phases and invertingor not inverting the signs of the sampled values.

Next, the sampling apparatus 10 begins the measurement by inputting thesignal under measurement (S210).

The band limiting section 110 allows the frequency components of theobservation band in the signal under measurement to pass through anddamps or restricts the frequency components that are outside of theobservation band. FIG. 3 shows an example where the pass band 320 is setin the band limiting section 110 to be a frequency band that is from 1.5times to 2.5 times the sampling clock frequency fs, and therefore theband limiting section 110 allows a signal under measurement to pass thatis centered on a frequency that is double the sampling clock frequencyfs. By allowing this signal under measurement 300 to pass and samplingthe signal under measurement 300 at a later stage, a negative frequencycomponent 310 is generated, which is centered on a frequency axis of 0and is symmetrical to the signal under measurement 300 on the negativefrequency side.

The clock control section 120 and the AD converters 125-1, 125-2 samplethe signal under measurement at a plurality of sampling phases atnon-uniform intervals for each sampling repetition cycle (S220). Morespecifically, the clock control section 120 generates a plurality ofsampling clocks having a plurality of phases at predeterminednon-uniform intervals to cancel out the replicas that are notobservation targets from among the replicas of the negative frequencycomponent of the signal under measurement and replicas of the signalunder measurement in the sampling band, for each sampling repetitioncycle. The plurality of AD converters 125 sample the signal undermeasurement with each of the plurality of sampling clocks.

The multiplexer 130 multiplexes the constant 0 and the sample dataoutput by each AD converter 125 in the order set by the setting section105, and outputs the thus multiplexed data (S225). The inverting section135 inverts the signs of the designated pieces of data in the sequenceof sample data received from the multiplexer 130, according to thesetting received from the setting section 105 (S230). The storagesection 140 stores the sequence of sample data output by the sampleprocessing section 115 (S235).

The Fourier transform section 155 Fourier transforms the sample datainto the frequency domain (S240). The extracting section 160 extractsthe target replicas in the frequency domain, and the frequencyconverting section 162 generates the signal under measurement in thefrequency domain based on the target replicas in the frequency domain(S245). Here, the extracting section 160 extracts the target replicas byeliminating the frequency components outside of the sampling band fromamong the components at each frequency obtained as a result of theFourier transform of the sample data. The frequency converting section162 reproduces the frequency components of the signal under measurementby frequency-shifting the target replicas to the observation band.

The inverse Fourier transform section 165 inverse Fourier transforms thefrequency components of the signal under measurement generated by thefrequency converting section 162 to obtain the digital waveform data ofthe signal under measurement (S250). The inverse Fourier transformsection 165 then outputs the waveform data of the signal undermeasurement (S255).

FIG. 4 shows a performance timing of the sample processing section 115according to the present embodiment.

The clock control section 120 outputs a sampling clock CLK1 having afrequency fs and a cycle 1/fs and a sampling clock CLK2 having afrequency fs and delayed by 1/(3fs) in relation to CLK1. The ADconverter 125-1 samples the signal under measurement by AD convertingthe signal under measurement input via the band limiting section 110,according to the rising timing of CLK1. The AD converter 125-2 samplesthe signal under measurement by AD converting the signal undermeasurement input via the band limiting section 110, according to therising timing of CLK2.

The multiplexer 130 outputs, for the first ⅓ of each cycle of thesampling clock, sample data D1(k) which is output by the AD converter125-1, where k is an integer. The multiplexer 130 outputs, for thesecond ⅓ of each cycle of the sampling clock, sample data D2(k) which isoutput by the AD converter 125-2. The multiplexer 130 outputs theconstant 0 for the final ⅓ of each cycle of the sampling clock. Theinverting section 135 inverts every other set of sample data output bythe AD converter 125-1 and the AD converter 125-2 to be negative. Morespecifically, the inverting section 135 outputs the sample data from theAD converter 125-1 and the AD converter 125-2 without inverting the signthereof at a certain cycle of the sampling clock, and then outputssample data having an inverted sign in the subsequent cycle of thesampling clock.

Through the process described above, the sample processing section 115outputs the output data D1(k) from the AD converter 125-1, the outputdata D2(k) from the AD converter 125-2, and the constant 0 in the statedorder within one cycle 1/fs of the signal under measurement 300 shown inFIG. 3. The sample processing section 115 then outputs, in thesubsequent cycle of the 1/fs of the signal under measurement 300, sampledata obtained by inverting the sign of D1(k+1) and D2(k+1).

FIG. 5 shows replicas generated in the signal under measurement sampledby the AD converter 125 according to the present embodiment. Asdescribed above, the inverting section 135 outputs sample data withoutinverting the signs thereof at a certain cycle in the sampling clock andthen outputs sample data having inverted signs at the subsequent cycle.Accordingly, the inverting section 135 outputs the sample data D1(k),D2(k), 0, −D1(k+1), and −D2(k+2) for each sampling repetition cycle,where one sampling cycle corresponds to two cycles of the samplingclock, namely a cycle of 2/fs.

Here, the AD converters 125-1, 125-2 sample the signal under measurementwith four sampling phases that are 0, 60, 180, and 240 degrees inrelation to the sampling repetition cycle (referred to hereinafter as“the first, second, third, and fourth sampling phases,” in the statedorder) for each sampling repetition cycle 2/fs. The inverting section135 inverts the signs of the values of the signal under measurementsampled at the sampling phases of 180 and 240 degrees, from among thesefour sampling phases. Here, one of the four sampling phases, forexample, the sampling phase of 0 degrees, is used for uniformundersampling with the sampling repetition cycle 2/fs, which means thatthe sampling repetition frequency is (½)fs.

In this case, replicas 510 a, 510 c, 510 d, 510 e, 510 f (also known as“aliases”) having frequency spectrums identical to the signal undermeasurement 300 occur at certain positions. These positions are found byfrequency-shifting the signal under measurement 300 within theobservation band from 1.5 fs to 2.5 fs, which is the positive frequencycomponent of the signal under measurement 300, by an integer multiple ofthe sampling repetition frequency (½)fs. Furthermore, replicas 520 a to520 f having frequency spectrums identical to the negative frequencycomponent 310 of the signal under measurement 300 occur at certainpositions. These positions are found by frequency-shifting the negativefrequency component 310 of the signal under measurement 300 within thefrequency band from −1.5 fs to −2.5 fs by an integer multiple of thesampling repetition frequency (½)fs. In this way, if a signal undermeasurement 300 that crosses integer multiples of (½)fs is sampled witha sampling repetition period (½)fs by the AD converters 125, thereplicas 510 of the signal under measurement 300 undesirably overlapwith the replicas 520 of the negative frequency component 310 of thesignal under measurement 300 on the frequency axis, so that it becomesdifficult to extract only one replica.

FIG. 6 shows frequency bands in which the replicas are canceled out bythe sample processing section 115 according to the present embodiment.As described above, the sample processing section 115 of the presentembodiment samples the signal under measurement at the first throughfourth sampling phases for each sampling repetition cycle 2/(fs). Here,if the sample processing section 115 samples the signal undermeasurement 300 at a plurality of different sampling phases, the phasedifference of the replicas occurring at positions found byfrequency-shifting the replicas by k times the sampling repetitionfrequency, with the signal under measurement as a base, is equal to ktimes the phase difference in the sampling repetition cycle. Here, k isan integer. For example, if the sample processing section 115 samplesthe signal under measurement at two sampling phases having a phasedifference of 60 degrees in the sampling repetition cycle, the replicasthat are shifted to a higher frequency by the sampling repetitionfrequency have a phase difference of 60 degrees, the replicas that areshifted to a higher frequency by double the sampling repetitionfrequency have a phase difference of 120 degrees, and the replicas thatare shifted to a higher frequency by triple the sampling repetitionfrequency have a phase difference of 180 degrees. Furthermore, thereplicas that are shifted to a lower frequency by the samplingrepetition frequency have a phase difference of −60 degrees, thereplicas that are shifted to a lower frequency by the samplingrepetition frequency have a phase difference of −120 degrees, and thereplicas that are shifted to a lower frequency by the samplingrepetition frequency have a phase difference of −180 degrees.

Accordingly, with the replicas 510 of the signal under measurement 300sampled at the first sampling phase as a base, which is the samplingphase that is 0 degrees in relation to the sampling process repletioncycle, the replicas 510 of the signal under measurement 300 sampled atthe second sampling phase have the signal under measurement 300 with afrequency centered on 2 fs as a base, and have a phase difference thatincreases by 60 degrees for every shift of (½)fs to a higher frequencyand decreases by 60 degrees for every shift of (½)fs to a lowerfrequency. In the same way, the replicas 510 of the signal undermeasurement 300 sampled at the third sampling phase have the signalunder measurement 300 as a base, and have a phase difference thatchanges by 180 degrees for every shift of the sampling repetitionfrequency. The replicas 510 of the signal under measurement 300 sampledat the fourth sampling phase have the signal under measurement 300 as abase, and have a phase difference that changes by 240 degrees for everyshift of the sampling repetition frequency.

Replicas having opposite phase differences, namely phase differences of180 degrees, are then added together to cancel each other out. Since thedata sampled at the third and fourth sampling phases has inverted signs,the four replicas centered on 0.5 fs, which are 0, 180, 180, and 0degrees, for example, cancel each other out. In the same way, the setsof four signals under measurement 300 or replicas 510 centered on eachfrequency shown in FIG. 6 that have “cancel” written next to them cancancel each other out.

FIG. 7A shows a signal under measurement input into the sampleprocessing section 115 of the present embodiment. FIG. 7B shows a signaloutput from the sample processing section 115. FIG. 7C shows areproduction of the frequency components 730 of the signal undermeasurement based on the synthesized replica 720 e.

As shown in FIG. 6, with the signal under measurement 300 as a base, thereplicas 510 that are shifted by an even integer multiple of thesampling repetition frequency (½)fs and the replicas 510 that areshifted by ±3 times the sampling repetition frequency (½)fs cancel eachother out. In this way, the signals under measurement 300 and thereplicas 510 with frequencies centered on 0, 0.5 fs, fs, 2 fs, 3 fs, andthe like cancel each other out, as shown in FIG. 7B. On the other hand,the replicas 510 that are centered on 1.5 fs, 2.5 fs, and the like areadded to each other instead of cancelling out, and so remain as thesynthesized replicas 710 a, 710 c, and the like.

In the same way, the replicas 520 of the negative frequency component310 of the signal under measurement 300 centered on 0, fs, 2 fs, 2.5 fs,3 fs, and the like cancel each other out. The replicas 520 that arecentered on 1.5 fs, 2.5 fs, and the like are added to each other insteadof cancelling out, and so remain as the synthesized replicas 720 a, 720e, and the like. Accordingly, only the synthesized replica 720 e remainsin the frequency band from 0 to a frequency less than fs, which is thesampling band in the present embodiment.

In this way, the setting section 105 can set a plurality of non-uniformsampling phases for the clock control section 120 such that the replicasthat are not observation targets cancel each other out, from among thereplicas of the negative frequency component and the replicas of thesignal under measurement in the observation band having a bandwidth lessthan that of the sampling band. The setting section 105 can also/insteadset the inverting section 135 to invert the signs of the values of thesignal under measurement sampled at at least one of the plurality ofsampling phases. Therefore, the clock control section 120 and theplurality of AD converters 125 can sample the signal under measurementwith a plurality of different phases that cancel out the replicas in thesampling band that are not observation targets, from among the replicasof the negative frequency component and the replicas of the signal undermeasurement in the observation band having a bandwidth less than that ofthe sampling band. The inverting section 135 can cancel out the replicasthat are not observation targets from among the replicas of the negativefrequency component and the replicas of the signal under measurement inthe sampling band by inverting the signs of the values of the signalunder measurement sampled at at least one of the plurality of samplingphases.

More specifically, if the replicas occur due to the signal undermeasurement or the negative frequency component being shifted by aninteger multiple, such as a multiple of −3, of the sampling repetitionfrequency, the setting section 105 may set a plurality of samplingphases for the clock control section 120. The plurality of samplingphases includes a first sampling set such that the time corresponding tothe aforementioned integer multiple of the phase difference is equal toa value obtained by adding ½ of a cycle to an integer multiple,including 0, of the sampling repetition cycle, and a second samplingphase that is different from the first sampling phase. These samplingphases may be 0 and 60 degrees respectively, for example. In order tocancel out the replicas caused by shifting the signal under measurementor the negative frequency component by an integer multiple, such as −3,of the sampling repetition frequency, the setting section 105 may firstset a plurality of sampling phases for the clock control section 120.The plurality of sampling phases may include a first and second samplingphase of 0 and 120 degrees respectively, for example, that cause theaforementioned integer multiple of the phase difference to be a multipleof the sampling repetition cycle. The setting section 105 may then setthe inverting section 135 to invert the signs of the values of thesignal under measurement sampled at the second sampling phase of 120degrees and to not invert the signs of the values of the signal undermeasurement sampled at the first sampling phase of 0 degrees.

The Fourier transform section 155 reads the sample data in the timedomain having the frequency spectrum shown above from the storagesection 140, and converts the sample data into the frequency domain. Inthis way, the Fourier transform section 155 obtains the sample data inthe frequency domain shown by FIG. 7B.

The extracting section 160 performs a band pass or low pass filteringprocess to extract the target synthesized replica 720 e in the samplingband from the sample data in the frequency domain. The frequencyconverting section 162 shifts the synthesized replica 720 e by afrequency of 1.5 fs to 2.5 fs, which is the observation band. If theobservation target is a replica of the negative frequency component 310of the signal under measurement 300 as in the present embodiment, thefrequency direction of the replica is inverted in relation to theoriginal signal under measurement 300, as shown by the synthesizedreplica 720 e in FIG. 7C. In this case, the extracting section 160 orthe frequency converting section 162 may reproduce the frequencyspectrum of the signal under measurement 300 by inverting the frequencydirection of the synthesized replica 720 e.

Since the synthesized replica 720 e overlaps with a plurality ofreplicas that are frequency shifted in relation to the originalfrequency component 310, the size and phase of the synthesized replica720 e may be different from those of the original frequency component310. For example, in the present embodiment, the four replicas 520 e ofthe negative frequency component 310 corresponding to the first throughfourth sampling phases have phases of 0, 300, 180, and 120 degrees, asshown in FIG. 6. These phases are obtained by shifting the replicas fromthe negative frequency component 310 by a frequency of 5 times thesampling repetition frequency (½)fs. When the first and second replicas520 e are added to each other and the third and fourth replicas 520 ecancel each other out, the resulting synthesized replica 720 e is 2√3times larger than the negative frequency component 310 and has a phasethat differs from that of the original frequency component 310 by 330degrees, which is equivalent to −30%. Accordingly, the extractingsection 160 or the frequency converting section 162 may adjust the sizeand phase of the synthesized replica 720 e in addition to the frequencyshift and frequency direction, in order to reproduce the signal undermeasurement 300.

The inverse Fourier transform section 165 obtains the waveform data ofthe signal under measurement in the time domain by inverse Fouriertransforming the signal under measurement 300 reproduced in thefrequency domain. Instead of adjusting the size and phase of thesynthesized replica 710e using the extracting section 160 or thefrequency converting section 162, the inverse Fourier transform section165 may adjust the size and phase of the waveform data of the signalunder measurement in the time domain.

As described above, the sampling apparatus 10 of the present embodimentsamples the signal under measurement with a plurality of sampling phasesat non-uniform intervals. The sampling apparatus 10 can then cancel outthe replicas in the sampling band that are not observation targets, fromamong the replicas of the negative frequency component and the replicasof the signal under measurement in the observation band having abandwidth that is less than the sampling bandwidth, by inverting thesigns of the values of the signal under measurement sampled at at leastone of the plurality of sampling phases as necessary. The samplingapparatus 10 reproduces the waveform data of the signal undermeasurement based on the remaining target replicas.

FIG. 8A shows another example of the signal under measurement input intothe sample processing section 115 of the present embodiment. FIG. 8Bshows another example of a signal output by the sample processingsection 115 of the present embodiment. A signal under measurement 800 ofthe present embodiment is positioned in an observation band having abandwidth of 1·fs and centered on a frequency a·fs, where “a” is anatural number. The following describes an example in which theplurality of AD converters 125 sample the signal under measurement witha plurality of sampling phases chosen from among phases obtained byuniformly dividing the sampling repetition cycle into a number n ofcycles that is larger than the number of sampling phases, which is 2 inthe present embodiment.

In this example, the setting section 105 sets, for the clock controlsection 120, the plurality of sampling phases chosen from among thephases obtained by uniformly dividing the sampling repetition cycle intothe number n of cycles that is larger than the number of samplingphases. More specifically, the setting section 105 sets the clockcontrol section 120 to generate sampling clocks CLK1 and CLK2respectively having a first sampling phase and a second sampling phase,which is delayed by (m/n)T in relation to the first sampling phase, foreach sampling repetition cycle T, where T=1/fs. Here, m and n arecoprime natural numbers. If m and n are not coprime, m and n can be setto be coprime by performing a fraction reduction of m and n and settingthe resulting values to be m and n.

In this case, f(t) of the signal under measurement and the digitalfunction shifting δ(t) can be used in Expression 1, shown below, tocalculate the sample data g₁(t) sampled by the AD converter 125-1 at thefirst sampling phase and the sample data g₂(t) sampled by the ADconverter 125-2 at the second sampling phase.

Expression 1:

${g_{1}(t)} = {\sum\limits_{k = {- \infty}}^{\infty}\;{{\delta\left( {t - {kT}} \right)}{f(t)}}}$${g_{2}(t)} = {\sum\limits_{k = {- \infty}}^{\infty}\;{{\delta\left( {t - {kT} - {\frac{m}{n}T}} \right)}{f(t)}}}$

The sample data g₁(t) and g₂(t) of Expression 1 are Fourier transformedto obtain the sample data G₁(ω) and G₂(ω) in the frequency domain, asshown below in Expression 2.

Expression 2:

${G_{1}(\omega)} = {\frac{1}{T}{\sum\limits_{k = {- \infty}}^{\infty}\;{F\left( {\omega - \frac{2\pi\; k}{T}} \right)}}}$${G_{2}(\omega)} = {\frac{1}{T}{\sum\limits_{k = {- \infty}}^{\infty}\;{{F\left( {\omega - \frac{2\pi\; k}{T}} \right)}{\exp\left( {{- j}{\frac{2\pi\; k}{T} \cdot \frac{m}{n}}T} \right)}}}}$

To simplify this example, it is assumed that the multiplexer 130 and theinverting section 135 output a waveform, obtained by adding togetherg₁(t) and g₂(t), to the storage section 140. More specifically, themultiplexer 130 outputs the sample data from the AD converter 125-1 atthe first sampling phase to the inverting section 135, outputs thesample data from the AD converter 125-2 at the second sampling phase tothe inverting section 135, and outputs the constant 0 to the invertingsection 135 at any other phases. The inverting section 135 outputs eachvalue of the sample data without inverting the sign thereof.

The sample data in the frequency band, which is obtained from theFourier transform section 155 Fourier transforming the sample dataoutput by the sample processing section 115, is made up of valuesobtained by adding together G₁(ω) and G₂(ω). Specifically, the Fouriertransform section 155 outputs the sample data of the frequency band asshown in Expression 3.

Expression 3:

${{G_{1}(\omega)} + {G_{2}(\omega)}} = {{\frac{1}{T}{\sum\limits_{k = {- \infty}}^{\infty}\;{{F\left( {\omega - \frac{2\pi\; k}{T}} \right)}\left( {1 + {\exp\left( {{- j}\frac{2m\;\pi\; k}{n}} \right)}} \right)}}} = {\frac{2}{T}{\sum\limits_{k = {- \infty}}^{\infty}\;{{F\left( {\omega - \frac{2\pi\; k}{T}} \right)}{\cos\left( \frac{m\;\pi\; k}{n} \right)}{\exp\left( {{- j}\frac{m\;\pi\; k}{n}} \right)}}}}}$

Expression 3 shows that, if cos(mπk/n) is equal to 0, G₁(ω) and G₂(ω)cancel out, so that the frequency band obtained as a summation of G₁(ω)and G₂(ω) is equal to 0. Here, the (a+1)th replicas of the negativefrequency component 810 should be set to cancel out, so that thereplicas of the negative frequency component 810 of the signal undermeasurement 800 cancel out in the sampling band having a bandwidth of1·fs and centered on the frequency fs. To achieve this, k should beequal to a+1 and cos(mπ(a+1)/n) should equal 0.

Here, when n is set equal to 2(a+1), mπ(a+1)/n=mπ(a+1)/{2(a+1)}=mπ/2.Since m and n are coprime and n is an even number, m is an odd number,and therefore cos(mπ/2)=0. Accordingly, if m is set to an odd numbersuch as 1 and n is set to 2(a+1), the replicas 830 of the negativefrequency component 810 in the sampling band centered on the frequencyfs cancel out. Therefore, the waveform generating section 150 canextract the replica 820 c of the signal under measurement 800 togenerate the waveform data of the signal under measurement.

As described above, if the signal under measurement centered on afrequency that is “a” times the sampling repetition frequency is shiftedto a lower frequency by (a−1) times the sampling repetition frequencyand the target replica is in the sampling band centered on the samplingrepetition frequency, two sampling phases should be used that areseparated by the odd number m, from among the phases obtained bydividing the sampling repetition cycle by n=2(a+1). In other words,these two sampling phases should have a phase difference of m/2(a+1)T.In the same way, if the negative frequency component of the signal undermeasurement centered on a frequency that is “a” times the samplingrepetition frequency is shifted to a higher frequency by (a+1) times thesampling repetition frequency and the target replica is based on thenegative frequency component and in the sampling band centered on thesampling repetition frequency, two sampling phases should be used thatare separated by the odd number m, from among the phases obtained bydividing the sampling repetition cycle by n=2(a−1). In other words,these two sampling phases should have a phase difference of m/2(a−1)T.

The setting section 105 can set the values of m and n such that thereplicas that are not observation targets cancel out to leave only thetarget replicas in the sampling band that are obtained by shifting thesignal under measurement in the observation band by any integer multipleof the sampling repetition frequency. More specifically, to cancel outthe replicas obtained by shifting the signal under measurement or thenegative frequency component by x times the sampling repetitionfrequency, the setting section 105 sets n equal to 2x and m equal to anodd number, for example. It should be noted that x must be greater thanor equal to 2 to achieve sampling at non-uniform intervals.

In order to cancel out the replicas in the sampling band that occur whenthe signal under measurement 800 or the negative frequency component 810is shifted by an integer multiple of the sampling repetition frequency,the setting section 105 may invert the signs of the values of the signalunder measurement sampled at at least one of the sampling phases asnecessary. By inverting the signs of the values of the signal undermeasurement, the setting section 105 can rotate the phase of thereplicas in the sampling band by 180 degrees.

Even if three or more sampling phases are used, the setting section 105can cancel out unnecessary replicas in the sampling band, set three ormore sampling phases that are suitable for allowing the target replicasto remain in the sampling band, and invert the signs of sample datacorresponding to one or more phases as necessary, in the same manner asdescribed above.

If m is an even number, the coprime n must be an odd number. In thiscase, cos(mπk/n) can not be equal to 0. Accordingly, if n is an oddnumber, the replicas do not cancel out. Even if n is an odd number,however, the sampling apparatus 10 according to the present embodimentcan still be realized as long as the value of n is large enough thatcos(mπk/n) can be treated as being equal to 0.

As described above, the sampling apparatus 10 of the present embodimentcan set the plurality of sampling phases at non-uniform intervalsaccording to the observation band, cancel out replicas in the samplingband that are not observation targets by inverting the signs of thesample data corresponding to at least one of the sampling phases asnecessary, and extract the target replicas to reproduce the waveformdata of the signal under measurement.

FIG. 9 shows a configuration of the sample processing section 115according to a first modification of the present embodiment. The sampleprocessing section 115 of the present modification adopts almost thesame function and configuration as the sample processing section 115shown in FIG. 1, and therefore components having substantially the sameconfiguration and function as components of the sample processingsection 115 of FIG. 1 are given the same reference numbers and thefollowing description omits all but differing points.

Instead of one inverting section 135 disposed behind the multiplexer130, as shown in FIG. 1, the sample processing section 115 according tothe present modification has a plurality of inverting sections 135-1 to135-N disposed to correspond to a plurality of AD converters 125-1 to125-N. The plurality of inverting sections 135-1 to 135-N are providedbetween the plurality of AD converters 125-1 to 125-N and themultiplexer 130. Each of the plurality of inverting sections 135-1 to135-N receives a setting from the setting section 105 to invert thesigns of the sample data values of the signal under measurement sampledby the corresponding AD converter 125 as necessary.

Each of the plurality of inverting sections 135-1 to 135-N may invertthe sign of the sample data output by the corresponding AD converter 125to be negative in every other sample. More specifically, each of theplurality of inverting sections 135-1 to 135-N may output the sampledata output by the corresponding AD converter 125 in a certain cycle ofthe sampling clock without inversion, and then invert the sign of thesample data in the subsequent cycle and output the inverted sample data.

In the present modification, the multiplexer 130 switches betweenselecting the constant 0 and the sample data from the plurality ofinverting sections 135-1 to 135-N. In this way, the multiplexer 130multiplexes the data and outputs the multiplexed sample data to thestorage section 140. The sample processing section 115 of the presentmodification can output the sample data in which the replicas in thesampling band that are not observation targets cancel out, in the sameway as the sample processing section 115 of FIG. 1.

FIG. 10 shows a configuration of the sample processing section 115according to a second modification of the present embodiment. The sampleprocessing section 115 according to the present modification adoptsalmost the same function and configuration as the sample processingsection 115 shown in FIG. 1, and therefore components havingsubstantially the same configuration and function as components of thesample processing section 115 of FIG. 1 are given the same referencenumbers and the following description omits all but differing points.

Instead of the clock control section 120 shown in FIG. 1, the sampleprocessing section 115 of the present modification has a plurality ofdelay circuits 1000-1 to 1000-N, a delay control section 1010, and aclock control section 1020. Each of the plurality of delay circuits1000-1 to 1000-N is disposed to correspond to one of the plurality of ADconverters 125-1 to 125-N. The plurality of delay circuits 1000-1 to1000-N are controlled by the delay control section 1010 to delay thesignal under measurement by an amount corresponding to each of theplurality of sampling phases. Each of the plurality of delay circuits1000-1 to 1000-N supplies the thus delayed signal under measurement tothe corresponding AD converter 125-1 to 125-N.

The delay control section 1010 receives a setting from the settingsection 105 to set the delay amounts of the plurality of delay circuits1000-1 to 1000-N to delay the signal under measurement by delay amountscorresponding to the plurality of sampling phases at non-uniformintervals, in relation to the sampling repetition cycle. Morespecifically, the delay control section 1010 sets the delay amounts ofthe plurality of delay circuits 1000-1 to 1000-N such that each delaycircuit 1000-1 to 1000-N delays the signal under measurement by anamount corresponding to the sampling phase in relation to the samplingrepetition cycle of the corresponding AD converter 125.

The delay control section 1010 may instead set the plurality of delaycircuits 1000-1 to 1000-N such that each delay circuit 1000-1 to 1000-Ndelays the signal under measurement by an amount corresponding to thephase difference between a reference phase in relation to the samplingrepetition phase and a sampling phase in relation to the samplingrepetition cycle of the corresponding AD converter 125. In this case,the delay circuit 1000-1 to 1000-N that corresponds to the AD converter125 having the earliest sampling phase can be omitted from theconfiguration of the sample processing section 115 if the referencephase in relation to the sampling repetition cycle is set as theearliest sampling phase from among the plurality of sampling phases.

The clock control section 1020 provides the plurality of AD converters125-1 to 125-N with reference clocks having the same phase. The clockcontrol section 1020 may provide the plurality of AD converters 125-1 to125-N with reference clocks having identical phases and cycles equal tothe sampling process repletion cycle.

The plurality of AD converters 125-1 to 125-N sample the signal undermeasurement delayed by the plurality of delay circuits 1000-1 to 1000-Naccording to the reference clock. Each of the plurality of AD converters125-1 to 125-N may sample the signal under measurement delayed by thecorresponding delay circuit 1000-1 to 1000-N with one of the referenceclocks having identical phases and cycles equal to the samplingrepetition cycle. The sample processing section 115 according to thepresent modification can output sample data in which the replicas in thesampling band that are not observation targets cancel out, in the sameway as the sample processing section 115 shown in FIG. 1.

FIG. 11 shows a configuration of the sample processing section 115according to a third modification of the present embodiment. The sampleprocessing section 115 according to the present modification adoptsalmost the same function and configuration as the sample processingsection 115 shown in FIG. 1, and therefore components havingsubstantially the same configuration and function as components of thesample processing section 115 of FIG. 1 are given the same referencenumbers and the following description omits all but differing points.

The sample processing section 115 according to the present modificationoutputs the sample data obtained by sampling the signal undermeasurement at sampling timings at non-uniform intervals obtained bythinning the reference clock. The sample processing section 115 of thepresent modification includes the AD converter 125, a data thinningsection 1100, and the inverting section 135.

The AD converter 125 samples the signal under measurement insynchronization with the reference clock. The data thinning section 1100thins the sample data output by the AD converter 125 according to thesetting from the setting section 105, and outputs the sample data at thesampling timings at non-uniform intervals. The data thinning section1100 supplies the thinned sample data to the inverting section 135.

In the present modification, the setting section 105 sets, for the datathinning section 1100 in the sample processing section 115, a samplingtiming in the sampling repetition cycle, which is an integer multiple ofthe reference clock, based on the observation band of the signal undermeasurement. The setting section 105 may set, for the data thinningsection 1100 in the sample processing section 115, a sampling timing ofthe data that remains in the sampling repetition cycle.

The setting section 105 sets, for the data thinning section 1100 in thesample processing section 115, the sampling timing in the samplingrepetition cycle such that the positional relationship between thesampling repetition cycle and the designated reference clock isidentical to the positional relationship between the sampling repetitioncycle and the designated reference clock in the sample processingsection 115 shown in FIG. 1. More specifically, the setting section 105sets, for the data thinning section 1100 in the sample processingsection 115, a sampling timing at determined non-uniform intervals suchthat one of the replicas of the signal under measurement in theobservation band and the replicas of the negative frequency component ofthe signal under measurement in the observation band remain, and thatall other replicas in the sampling band cancel out.

The setting section 105 may set, for the data thinning section 1100 inthe sample processing section 115, a plurality of reference clock phasesselected from among the phases obtained by uniformly dividing thesampling repetition cycle into a number n of cycles that is larger thanthe number of reference clock phases. More specifically, the settingsection 105 may set the data thinning section 1100 such that the sampledata of the first reference clock phase and sample data of the secondreference clock phase, which is delayed by (m/n)T in relation to thephase of the first reference clock, remain in each sampling repetitioncycle T, where T=1/fs. Here, m and n are set to be coprime naturalnumbers. If m and n are not coprime, m and n can be set to be coprime byperforming a fraction reduction of m and n and setting the resultingvalues to be m and n. Furthermore, the setting section 105 may set theinverting section 135 to output the values of the sample data withoutinverting the signs.

The sample processing section 115 of the present modification can outputthe sample data in which the replicas in the sampling band that are notobservation targets cancel out. The sample processing section 115 of thepresent modification can decrease the necessary storage capacity and thedata transmission amount in the final stage of the data processing bythinning the sample data output by the AD converter 125 to be the datarate necessary for reproducing the signal under measurement in theobservation band. In this way, the sample processing section 115 of thepresent modification can be implemented to reduce the size of thecircuit connected at the final stage.

FIG. 12 shows a configuration of the sample processing section 115according to a fourth modification of the present embodiment. The sampleprocessing section 115 according to the present modification adoptsalmost the same function and configuration as the sample processingsection 115 shown in FIG. 11, and therefore components havingsubstantially the same configuration and function as components of thesample processing section 115 of FIG. 11 are given the same referencenumbers and the following description omits all but differing points.

Instead of the data thinning section 1100 shown in FIG. 11, the sampleprocessing section 115 of the present modification has a clock thinningsection 1200 in the sample processing section 115. The sample processingsection 115 of the present modification outputs the sample data obtainedby sampling the signal under measurement at sampling timings atnon-uniform intervals obtained by thinning the reference clock, in thesame manner as the sample processing section 115 shown in FIG. 11.

The clock thinning section 1200 thins the reference clock according tothe setting from the setting section 105 to output a sampling clock withnon-uniform intervals. The AD converter 125 outputs sample data obtainedby sampling the signal under measurement in synchronization with thesampling clock supplied from the clock thinning section 1200. The ADconverter 125 outputs the sample data to the inverting section 135.

The setting section 105 of the present modification sets the clockthinning section 1200 in the same way as the data thinning section 1100shown in FIG. 11. In other words, the setting section 105 sets, for theclock thinning section 1200 in the sample processing section 115, thesampling timing in the sampling repetition cycle that is an integermultiple of the cycle of the reference clock, based on the observationband of the signal under measurement.

The sample processing section 115 of the present modification can outputthe sample data in which the replicas in the sampling band that are notobservation targets cancel out, in the same way as the sample processingsection 115 shown in FIG. 11. The sample processing section 115 of thepresent modification can decrease the necessary storage capacity and thedata transmission amount in the final stage of the data processing,thereby reducing the size of the circuit connected at the final stage.

While the embodiments of the present invention has have been described,the technical scope of the invention is not limited to the abovedescribed embodiments. It is apparent to persons skilled in the art thatvarious alterations and improvements can be added to the above-describedembodiments. It is also apparent from the scope of the claims that theembodiments added with such alterations or improvements can be includedin the technical scope of the invention.

For example, instead of including the Fourier transform section 155, theextracting section 160, the frequency converting section 162, and theinverse Fourier transform section 165, the waveform generating section150 may include a low pass filter that allows a frequency component thatis less than or equal to a preset frequency to pass through, from amongthe sample data read from the storage section 140. In this way, thewaveform generating section 150 can output waveform data in thefrequency band obtained by frequency converting the signal undermeasurement in the observation band. The waveform generating section 150may include a multiplier that multiplies the waveform data output fromthe low pass filter by sine wave data. The sine wave data may have afrequency equal to the frequency of the observation band plus or minusthe frequency of the sampling band. In this way, the waveform generatingsection 150 can reproduce the signal under measurement by frequencyconverting the waveform data in the sampling band output by the low passfilter into waveform data in the observation band.

The sample processing section 115 may be provided with a sample/holdcircuit or a track/hold circuit at a stage prior to each of theplurality of sample processing sections 115. In this way, the sampleprocessing section 115 can more accurately sample the signal undermeasurement.

FIG. 13 shows an example of a hardware configuration of a computer 1900according to the present embodiment. The computer 1900 according to thepresent embodiment is provided with a CPU peripheral including a CPU2000, a RAM 2020, a graphic controller 2075, and a display apparatus2080, all of which are connected to each other by a host controller2082; an input/output section including a communication interface 2030,a measurement interface 2032, a hard disk drive 2040, and a CD-ROM drive2060, all of which are connected to the host controller 2082 by aninput/output controller 2084; and a legacy input/output sectionincluding a ROM 2010, a flexible disk drive 2050, and an input/outputchip 2070, all of which are connected to the input/output controller2084.

The host controller 2082 is connected to the RAM 2020 and is alsoconnected to the CPU 2000 and graphic controller 2075 accessing the RAM2020 at a high transfer rate. The CPU 2000 operates to control eachsection based on programs stored in the ROM 2010 and the RAM 2020. Thegraphic controller 2075 acquires image data generated by the CPU 2000 orthe like on a frame buffer disposed inside the RAM 2020 and displays theimage data in the display apparatus 2080. In addition, the graphiccontroller 2075 may internally include the frame buffer storing theimage data generated by the CPU 2000 or the like.

The input/output controller 2084 connects the communication interface2030 serving as a relatively high speed input/output apparatus, and thehard disk drive 2040, and the CD-ROM drive 2060 to the host controller2082. The communication interface 2030 communicates with otherapparatuses via a network.

The measurement interface 2032 communicates with the sample processingsection 115 of the present embodiment. The measurement interface 2032supplies setting data and control data to the sample processing section115, and acquires sample data sampled by the sample processing section115. The measurement interface 2032 may communicate with the bandlimiting section 110 of the present embodiment to set the passablefrequency band for the band limiting section 110.

The hard disk drive 2040 stores the programs and data used by the CPU2000 housed in the computer 1900. The CD-ROM drive 2060 reads theprograms and data from a CD-ROM 2095 and provides the read informationto the hard disk drive 2040 via the RAM 2020.

Furthermore, the input/output controller 2084 is connected to the ROM2010, and is also connected to the flexible disk drive 2050 and theinput/output chip 2070 serving as a relatively high speed input/outputapparatus. The ROM 2010 stores a boot program performed when thecomputer 1900 starts up, a program relying on the hardware of thecomputer 1900, and the like. The flexible disk drive 2050 reads programsor data from a flexible disk 2090 and supplies the read information tothe hard disk drive 2040 via the RAM 2020. The input/output chip 2070connects the flexible disk drive 2050 to the input/output controller2084 along with each of the input/output apparatuses via, a parallelport, a serial port, a keyboard port, a mouse port, or the like.

The programs provided to the hard disk drive 2040 via the RAM 2020 arestored in a storage medium, such as the flexible disk 2090, the CD-ROM2095, or an IC card, and provided by a user. The programs are read fromstorage medium, installed in the hard disk drive 2040 inside thecomputer 1900 via the RAM 2020, and performed by the CPU 2000.

The programs installed in the computer 1900 to make the computer 1900function as a portion of the sampling apparatus 10 are provided with aninput module, a setting module, a storage module, and a waveformgenerating module. These programs and modules prompt the CPU 2000 or thelike to make the computer 1900 function as the input section 100, thesetting section 105, the storage section 140, and the waveformgenerating section 150, respectively.

The information processes recorded in these programs are read by thecomputer 1900 to cause the computer 1900 to function as software andhardware described above, which are exemplified by the specific sectionsof the input section 100, the setting section 105, the storage section140, and the waveform generating section 150. With these specificsections, a unique sampling apparatus 10 suitable for an intended usecan be configured to function along with the band limiting section 110and the sample processing section 115 by realizing the calculations orcomputations appropriate for the intended use of the computer 1900 ofthe present embodiment.

For example, if there is communication between the computer 1900 and anexternal apparatus or the like, the CPU 2000 performs the communicationprogram loaded in the RAM 2020, and provides the communication interface2030 with communication processing instructions based on the content ofthe process recorded in the communication program. The communicationinterface 2030 is controlled by the CPU 2000 to read the transmissiondata stored in the transmission buffer area or the like on the storageapparatus, such as the RAM 2020, the hard disc 2040, the flexible disk2090, or the CD-ROM 2095, and send this transmission data to thenetwork, and to write data received from the network onto a receptionbuffer area on the storage apparatus. In this way, the communicationinterface 2030 may transmit data to and from the storage apparatusthrough DMA (Direct Memory Access). As another possibility, the CPU 2000may transmit the data by reading the data from the storage apparatus orcommunication interface 2030 that are the origins of the transmitteddata, and writing the data onto the communication interface 2030 or thestorage apparatus that are the transmission destinations.

The CPU 2000 may perform various processes on the data in the RAM 2020by reading into the RAM 2020, through DMA transmission or the like, allor a necessary portion of the database or files stored in the externalapparatus such as the hard disk 2040, the CD-ROM drive 2060, the CD-ROM2095, the flexible disk drive 2050, or the flexible disk 2090. The CPU2000 writes the processed data back to the external apparatus throughDMA transmission or the like. In this process, the RAM 2020 isconsidered to be a section that temporarily stores the content of theexternal storage apparatus, and therefore the RAM 2020, the externalapparatus, and the like in the present embodiment are referred to as amemory, a storage section, and a storage apparatus. The variety ofinformation in the present embodiment, such as the variety of programs,data, tables, databases, and the like are stored on the storageapparatus to become the target of the information processing. The CPU2000 can hold a portion of the RAM 2020 in a cache memory and read fromor write to the cache memory. With such a configuration as well, thecache memory serves part of the function of the RAM 2020, and thereforethe cache memory is also included with the RAM 2020, the memory, and/orthe storage apparatus in the present invention, except when adistinction is made.

The CPU 2000 executes the various processes such as the computation,information processing, condition judgment, searching for/replacinginformation, and the like included in the present embodiment for thedata read from the RAM 2020, as designated by the command sequence ofthe program, and writes the result back onto the RAM 2020. For example,when performing condition judgment, the CPU 2000 judges whether avariable of any type shown in the present embodiment fulfills acondition of being greater than, less than, no greater than, no lessthan, or equal to another variable or constant. If the condition isfulfilled, or unfulfilled, depending on the circumstances, the CPU 2000branches into a different command sequence or acquires a subroutine.

The CPU 2000 can search for information stored in a file in the storageapparatus, the database, and the like. For example, if a plurality ofentries associated respectively with a first type of value and a secondtype of value are stored in the storage apparatus, the CPU 2000 cansearch for entries fulfilling a condition designated by the first typeof value from among the plurality of entries stored in the storageapparatus. The CPU 2000 can then obtain the second type of valueassociated with the first type of value fulfilling the prescribedcondition by reading the second type of value stored at the same entry.

The programs and modules shown above may also be stored in an externalstorage medium. The flexible disk 2090, the CD-ROM 2095, an opticalstorage medium such as a DVD or CD, a magneto-optical storage medium, atape medium, a semiconductor memory such as an IC card, or the like canbe used as the storage medium. Furthermore, a storage apparatus such asa hard disk or RAM that is provided with a server system connected tothe Internet or a specialized communication network may be used toprovide the programs to the computer 1900 via the network.

1. A sampling apparatus that samples a signal under measurement,comprising: a sampling section that samples the signal under measurementat a plurality of sampling phases at non-uniform intervals for eachsampling repetition cycle; and an inverting section that cancels out areplica that is not an observation target, from among replicas in asampling band of the signal under measurement and the replicas in thesampling band of a negative frequency component of the signal undermeasurement, by inverting a sign of a value of the signal undermeasurement sampled at at least one of the plurality of sampling phases.2. The sampling apparatus according to claim 1, further comprising aclock control section that generates a plurality of sampling clocks at aplurality of sampling phases at non-uniform intervals for each samplingrepetition cycle, wherein the sampling section samples the signal undermeasurement with each of the plurality of sampling clocks.
 3. Thesampling apparatus according to claim 1, further comprising a pluralityof delay circuits that delay the signal under measurement by delayamounts corresponding to the plurality of sampling phases, wherein thesampling section samples the signal under measurement delayed by each ofthe plurality of delay circuits, according to a reference clock.
 4. Thesampling apparatus according to claim 1, further comprising a settingsection that sets the phases at which the signs of the values of thesignal under measurement are inverted by the inverting section.
 5. Thesampling apparatus according to claim 4, further comprising an inputsection that receives an observation band of the signal undermeasurement as input, wherein the setting section sets whether theinverting section inverts the signs of the values of the signal undermeasurement sampled at each of the plurality of sampling phases, basedon the observation band.
 6. The sampling apparatus according to claim 4,wherein in order to cancel out the replica that is generated by shiftingthe signal under measurement or the negative frequency component by aninteger multiple of a sampling repetition frequency, the setting sectionsets the inverting section to invert the sign of the value of the signalunder measurement sampled at a second sampling phase and to not invertthe sign of the value of the signal under measurement sampled at a firstsampling phase, where the first sampling phase is set such that a timecorresponding to said integer multiple of a phase difference becomesequal to an integer multiple of the sampling repetition cycle and thesecond sampling phase is different from the first sampling phase.
 7. Thesampling apparatus according to claim 1, further comprising: a Fouriertransform section that Fourier transforms an output signal from theinverting section into the frequency domain; an extracting section thatextracts the replica that is an observation target in the frequencydomain; a frequency converting section that converts the signal undermeasurement into the frequency domain, based on the replica that is theobservation target in the frequency domain; and an inverse Fouriertransform section that generates waveform data of the signal undermeasurement in the time domain by inverse Fourier transforming thesignal under measurement converted into the frequency domain.
 8. Thesampling apparatus according to claim 2, wherein the sampling sectionincludes a plurality of samplers that are disposed to correspondone-to-one with a plurality of sampling clocks, and that each sample thesignal under measurement with the corresponding sampling clock.
 9. Thesampling apparatus according to claim 1, wherein the sampling sectionsamples the signal under measurement at the plurality of sampling phasesselected from among phases obtained by uniformly dividing the samplingrepetition cycle into a number of cycles greater than a number of thesampling phases.
 10. A method for sampling a signal under measurementwith a sampling apparatus, the method comprising the steps of: sampling,by a sampling section of the sampling apparatus, the signal undermeasurement at a plurality of sampling phases at non-uniform intervalsfor each sampling repetition cycle; and canceling out, by an invertingsection of the sampling apparatus, a replica that is not an observationtarget, from among the replicas in a sampling band of the signal undermeasurement and the replicas in the sampling band of a negativefrequency component of the signal under measurement, by inverting a signof a value of the signal under measurement sampled at at least one ofthe plurality of sampling phases.
 11. A non-transitory recording mediumstoring thereon a program that, when performed by a computer, causes thecomputer to perform operations comprising: sample a signal undermeasurement at a plurality of sampling phases at non-uniform intervalsfor each sampling repetition cycle; and cancel out a replica that is notan observation target, from among the replicas in a sampling band of thesignal under measurement and the replicas in the sampling band of anegative frequency component of the signal under measurement, byinverting a sign of a value of the signal under measurement sampled atat least one of the plurality of sampling phases.